Hi, Garageboy.
The answer will also depend on what Vf of those Lux I and Lux IIIs are. Given the same xxxJ bin, then a Lux I R bin will have more lumens/watt than the Lux III T/S bin. Just off top my head, I would think the TxxJ and RxxJ will give off just about the same level of light around 400ma, given Lux I has higher lumens/watt. But thesurefire had a good point, you could always retrieve the lux III later for another use if you prefer.
Another consideration is the 'tint' shift when a lux is underdriven(here will be the Lux IIIs). For example, even though a lux III TW0J will be a (tiny bit of warm) white, when it is underdriven, it could appear warmer(or more yellowish).